Problem: Solve for $x$ and $y$ using elimination. ${-3x+y = -19}$ ${-5x-2y = -39}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ ${-6x+2y = -38}$ $-5x-2y = -39$ Add the top and bottom equations together. $-11x = -77$ $\dfrac{-11x}{{-11}} = \dfrac{-77}{{-11}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-3x+y = -19}\thinspace$ to find $y$ ${-3}{(7)}{ + y = -19}$ $-21+y = -19$ $-21{+21} + y = -19{+21}$ ${y = 2}$ You can also plug ${x = 7}$ into $\thinspace {-5x-2y = -39}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 2y = -39}$ ${y = 2}$